7 Measuring Low Current Noise Levels

Placing a resistance on the non-inverting input of the op amp will translate current noise to voltage noise. Furthermore, when this resistor is increased so that $R_s>4kT/{\left(i_n\right)}^2$ then current noise will be the dominant noise source. However, as discussed previously, when R_s is increased to be very large, the noise bandwidth and signal bandwidth of the amplifier is limited, so the increasing current noise from f-squared noise may not be significant. It is, however, possible to mathematically correct for the bandwidth limitations and subtract thermal noise from the source resistor to reveal the current noise over frequency. The following is a procedure that can be used to measure low levels of current noise and correct for the parasitic impedance. Table 7-1 defines the variables used in the test procedure.

1. Select a resistor that according to the bias current of the device. Bias current multiplied by the source impedance will set the DC voltage at amplifiers input. In this example we will choose 10 GΩ. This sets the output offset to 100 mV worst case for OPA350 (IB×Rs = 10 pA×10 GΩ = 100 mV). The low frequency current noise for this device is 0.5 fA/√Hz, so the source resistor maintains that current noise dominates ( $R_s>4kT/{\left(i_n\right)}^2=6.59G\Omega$ ).
2. Calibrate the noise floor of measurement system (for example, spectrum analyzer). This is done by measuring the noise without the amplifier installed. This reading can be subtracted from the noise measurement to correct for the noise floor.
3. Install the amplifier and measure the output noise.
4. The following steps mathematically correct for the thermal noise and for the parasitic impedance from the device and parasitic capacitance.
5. Determine the closed loop gain of the buffer: $G_{cl}=1/[{\left(f/GBW\right)}^2+1]$
6. Divide output noise by the close loop gain: $e_{nRTI}=e_{nOUT}/G_{cl}$
7. Determine the impedance of the common mode and parasitic capacitance over frequency: $X_{ccm}=1/(2\pi {(C}_{cm}+C_{par})f)$
8. Find the source resistor noise: $e_{nr}=\sqrt{4kT{R}_s}$
9. Find the source resistor noise at amplifiers input: $e_{nrRTI}=e_{nr}\left(X_{ccm}/\sqrt{{X_{ccm}}^2+{R_s}^2}\right)$
10. Calculate the voltage noise at the amplifiers input from the current noise sources only. Do this by subtracting the amplifier voltage noise and source resistors thermal noise from measured noise RTI: $e_{n\_current}=\sqrt{{\left(v_{nRTI}\right)}^2-{\left(e_{nrRTI}\right)}^2-{\left(e_{nAmp}\right)}^2}$ . For the OPA320, the amplifier noise is 5nV/√Hz, so the calculation is: $e_{n\_current}=\sqrt{{\left(step6 \right)}^2-{\left(step9\right)}^2-{\left(5nV/\sqrt{Hz}\right)}^2}$ . Figure 7-1 shows the results from each step over frequency.
11. Calculate the impedance seen looking from the non-inverting input to ground. This is the impedance that the voltage noise from step 10 sees. This is the parallel combination of the source resistance and reactance of the input capacitance. $Z_{input}=R_s{X}_{ccm}/\sqrt{{X_{ccm}}^2+{R_s}^2}$
12. Calculate input current noise: $i_n=e_{n\_current}/Z_{input}$

Figure 7-1 Voltage Noise Components Used in Current Noise Calculation

Figure 7-2 Final Current Noise Based on Measured Amplifier Output Noise